Question

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Answer 1

Answer:

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Step-by-step explanation:

1.

as here angle dob=160

angle dob=m (arc db)

because measure of central angle is same as that of its opposite intercepted arc

so then m (major arc db)=360-m (minor arc db)

ie major arc db=360-160=200

now then here angle dpb intercepts major arc

so then angle dpb=half of m (major arc db)

because of inscribed angle theorem

so angle dpb=1/2×200

ie angle dpb=100 degree

3.

now here angle pqs=angle qsr=x degree (given) (1)

now here angle qrt and qrs forms linear pair

hence angle qrt+qrs =180

ie angle qrs=180-65 (angle qrt=65)

so angle qrs=115

now consider triangle qsr

apply sum of angles in triangle property

we get

angle qsr+qrs+sqr=180

so here angle sqr=28 (given)

so angle qsr+115+28=180

hence angle qsr=37 (2)

thus angle pqs=37 (from 1) (3)

so now in triangle qps

angle qps=90 (given) (4)

so then angle qps+pqs+psq=180

then angle psq+90+37=180 (from 3 and 4)

so angle psq=180-127

ie angle psq=53 degree

hence angle psq is 53 degre